Effect of the renormalization group on the symmetry breaking patterns of SU(n) Higgs potentials

As a first step toward the study of the effects of radiative corrections on spontaneously broken potentials we consider the renormalization group equations for those parameters which determine the shape of the potential and the symmetry breaking patterns. As examples we consider the Higgs potential for a single scalar field and for the adjoint represention of SU(n). In the latter case we also obtain some results at the classical level - a new proof of the Michel conjecture, the Higgs mass spectrum and an explicit expression for the parameter that determines the symmetry breaking pattern.